Articles of math software

Find generators of a group in GAP

This is a question in the mathematical software called GAP: What is the command for displaying all the generators of a given group? I have been searching around but yet not found anything helpful, so I am hoping I will get a quick response here.

Software for generating Cayley graphs of $\mathbb Z_n$?

Does it exist any program (for linux) which can generate a nice Cayley graph of any $\mathbb Z_n$? (If it’s possible to create such a graph at all, that is.) (where perhaps $n ≤ 100$ or something like that)

How do I substitute a value into a polynomial in GAP?

Question: How do I substitute a value into a polynomial in GAP? So, if I start off with the following: x:=Indeterminate(Integers,”x”); f:=x^2+3; I have $f$ as the polynomial $x^2+3$ over the integers. How can I find, say, $f(100)$? There should be a simple one line answer, but I can’t seem to find it in the […]

FLOSS tool to visualize 2- and 3-space matrix transformations

I’m looking for a FLOSS application (Windows or Ubuntu but preferably both) that can help me visualize matrix transformations in 2- and 3-space. So I’d like to be able to enter a vector or matrix, see it in 2-space or 3-space, enter a transformation vector or matrix, and see the result. For example, enter a […]

If $h$ divides $|G|$, not necessary that $G$ has a subgroup of order $h$

if $h$ divides $\# G$, then it is not necessarily that $G$ has a subgroup of size $h$ which can be related to Lagrange Theorem $[G:H]=\frac{\#G}{\# H}$ in the case when the subgroup exists, however it is not generally true such as in the case of $\mathbb A_4$ with order of 12 and having no […]

Is a function in an ideal? Verification by hand and Macaulay 2

Suppose $$f_1=-4x^4y^2z^2+y^6+3z^5,$$ $$f_2=-4x^2y^2z^2+y^6+3z^5,$$ $$f_3=4x^4y^2z^2+y^6+3z^5,$$ $$f_4=4x^2y^2z^2+y^6+3z^5$$ and $$I=\langle xz-y^2,x^3-z^2\rangle\subset\mathbb C[x,y,z].$$ Is $f_i\in I?$ The answer is Yes in some cases. The question can be checked with Macaulay 2: when the remainder is zero with respect to the Gröbner basis like (R=QQ[x,y,z]; fi=…; I=ideal(x*z-y^2,x^3-z^2); G=gb(I);f%G returning zero, $f_i\not\in I$. Division with respect to the elements in ideal […]

Does anyone know of any open source software for drawing/calculating the area of intersection of different shapes?

I would like to be able to draw any number of different shapes and determine the area of their intersections. I’m looking for free, open source software. I thought about trying to code something up myself, but it would save a lot of time and trouble if there is something out there that can do […]

free software to create equations and export to various formats

I’m looking for free software to create equations, and then be able to export to formats such as .jpg, .pdf, or maybe even MathML. Open source is nice but not required, internet based would be great but a local installed application would work as well. Being able to create graphs would be a positive, but […]

inverse Laplace transfor by using maple or matlab

I want to use inverse Laplace transform to F function by using maple or matlab. However I cannot get any answer. I know the answer from table but I want to use one of softwares. from table: $$\mathscr{L}^{-1}({1\over \sqrt{p}}~ e^{-\sqrt{p~a}}~\cos(\sqrt{p~a}))={1\over \sqrt{\pi~t}}~\cos \left({a \over 2t} \right)$$ Maple: with(inttrans); F := (p^(-1/2))*exp(-(p*a)^(1/2))*cos((p*a)^(1/2)); f := invlaplace(F, p, t); […]

Intuitive significance open sets (and software for learning topology?)

I have just started to learn topology and I referred to some books and online lectures. The problem is that they all talk the same things and are missing the same things. I want to know “what is the intuitive significance of open set that makes it so important to be studied?” I read reasons […]